Research on Damage Evolution in Ultra-thin Sheet Material under Deep Drawing and Ironing Process

In this paper, the effect of damage induced in deep drawing and ironing processes on the subsequent service performance of deep drawn cups was investigated. To obtain the cups with different amount of deformation damage, three kinds of drawing tests including one-stage deep drawing, two-stage deep drawing, and two-stage deep drawing and ironing were conducted using a 0.3 mm interstitial-free steel sheet. With help of the DF2015 ductile fracture model, the damage evolution of the drawn cups was calculated. Moreover, ring specimens cut from the side walls of the drawn cups were tested in a specially designed tension platform. The load F max and displacement x corresponding to the maximum load point, and the difference in displacement dx from the maximum load point to the fracture initiation point of ring tensile specimens were used as indicators to evaluate the effect of accumulated damage on the subsequent service performance of the parts.


Introduction
Deep drawing process is a sheet metal forming process widely used in automotive, aerospace and other fields.Based on the global requirement of energy saving and carbon emission reduction, the demand for automotive parts light-weighting technology has become higher.The process of deep drawing followed by ironing can reduce the thickness of parts, presenting an effective way of light-weighting.Material experiences large deformation in deep drawing and ironing process, which results in non-negligible deformation damage to the material [1].The knowledge of damage evolution and its effect on subsequent service performance of drawn cups is of great important.Many researchers have investigated the deep drawing process of sheet material by combining theoretical analysis and numerical simulation.Zhang et al. [2] carried out a two-stage deep drawing test to study the effect of different hardening models and the strain path change on the prediction accuracy of deep drawing process.Gorji and Mohr [3] performed experiments on the deep drawing of triangular parts and evaluated tension-shear fracture in the forming process using simulations combining Yld-2000 plasticity with Hosford-Coulomb fracture model.Kim and Hong [4] developed a stress triaxiality failure diagram for Al3003 sheet and used the generalized incremental stress state dependent damage model to predict shear fracture in multi-stage forming of the rectangular cup.Basak and Panda [5] predicted the failure IOP Publishing doi:10.1088/1757-899X/1307/1/012008 2 limits of AA5052 sheets by various uncoupled fracture criteria and performed experiments containing two-stage deep drawing to evaluate the forming limits under nonlinear strain paths.Based on the Lemaitre model, Mueller and Herrig [6] investigated the effect of different loading paths on the damage evolution and distribution in the material during classical deep drawing, multistep deep drawing and reverse deep drawing processes.During the sheet metal forming process damage such as micro-holes and micro-cracks can occur in the interior of parts under a combined effect of material properties, external loads and microstructure.Similar to work-hardening and residual stresses, forming induced damage also affects the mechanical properties of the product [7].Metal forming is focused on creating products with known mechanical properties [8], so it is necessary to explore the effect of damage during the forming process on product properties.Besserer et al. [9] investigated the damage evolution and fatigue behavior of orbital forming parts and concluded that damage has a detrimental effect on fatigue life.Tekkaya et al. [10] excluded the interference of strain hardening and residual stresses and demonstrated experimentally for the first time the separate effect of damage on the fatigue strength of extrusions and bends.Fayolle et al. [11] accurately predicted the damage modes of self-piercing riveted joints by using the damage obtained through the continuum damage mechanics model as an input to the mechanical strength simulation of the parts.The aim of this study is to investigate the damage evolution during deep drawing and ironing processes of ultra-thin sheets, as well as the effect of damage induced in the forming processes on the mechanical properties of the cylindrical cups.A 0.3 mm interstitial-free (IF) steel was selected as the studied material.Firstly, different deep drawing forming tests containing one-stage deep drawing (OSDD), twostage deep drawing (TSDD) and two-stage deep drawing and ironing (TSDDI) were carried out.Finite element simulations were conducted to obtain the damage evolution of the material under the three drawing processes by utilizing the fracture locus determined in previous work [12].Subsequently, tension tests on ring specimens cut from the deep-drawn cylindrical cups were designed and carried out to evaluate the effect of damage on the subsequent service properties of the material.

Deep drawing and ironing test
The material studied in this paper is 0.3mm IF steel, and the mechanical properties of the material in the rolling direction measured by uniaxial tensile experiments are shown in Table 1.Three kinds of deep drawing tests containing OSDD, TSDD, and TSDDI were carried out to involve different amounts of deformation and damage in the drawn cups.The schematic diagrams and die structures of the three deep drawing processes are shown in Fig. 1.The final diameter of the cups obtained from OSDD and TSDD was the same.Meanwhile, the cups with different thickness reduction rates (TRRs) were achieved in TSDDI using various punches with different diameters and a fixed die geometry.The material of punches and dies for the deep drawing tests was Cr12MoV, and the Rockwell hardness of the material after quenching treatment was about HRC 55~58.The deep-drawing dies were assembled on the SANS CMT5305 testing machine.Before starting the tests, sandpaper and alcohol were used to remove rust and oil and other debris from the surface of the specimen, and zinc stearate lubricant was applied to the tool surfaces and specimens.The tests were carried out on blanks with diameters of 44 mm, 46 mm, and 48 mm at a loading speed of 10 mm/min and more than three parallel tests were conducted for each size of blank.In OSDD and the first stage of TSDD and TSDDI, three nitrogen gas springs were used to provide a blank holder force of approximately 11kN; no blank holder was required in the second stage of TSDD and TSDDI.To analyse the deformation and damage evolution during deep drawing process, finite element simulation was performed based on ABAQUS/Explicit software.Considering the geometric symmetry of the models, two-dimensional axisymmetric deep drawing forming models were constructed.The blank was meshed as the axisymmetric linear reduction element CAX4R with a length of 0.06 mm and the tools were set as analytical rigid bodies.The damage was defined using the DF2015 model, in which the equivalent plastic strain, stress triaxiality and maximum shear stress are assumed to control the void nucleation, growth and coalescence.The expression of DF2015 model is presented in Eqs. ( 1) and (2).
(3 ) ( , , ) 0 3 3 where , L, and f  are stress triaxiality, Lode parameter, and fracture strain, respectively; Ci (i =1-4) and C are material constants needed to be identified.The material constants were calibrated using the surface fitting method between DF2015 model and the fracture limit obtained from Nakajima test.The detailed calibration procedure can be referred to the previous work [12].The values are C1=2.4516,C2=0.5641,C3=0.7419,C4=-0.6764 and C=2/3.For non-proportional strain paths, the accumulated damage (D) can be obtained from the integral form of DF2015 model as seen in Eq. ( 3).The fracture occurs when D = 1.

Ring specimen tension test
To evaluate the damage of the cups produced in different process routines, tension testing of ring specimen was designed and carried out.As shown in Fig. 2(a), the ring-shaped specimen was cut from the middle section of the side wall in the deep drawn cup since the deformation in this region is more uniform.Fig. 2(b) demonstrates the ring tension test platform, where the D-shaped blocks were placed inside the specimen and clamped with the upper and lower holdings to ensure that the scalar segment of the ring specimen was free from contact.The loading speed of ring specimen tension test was set as 0.36 mm/min.Through comparing the force and displacement curves, the effect of damage on the mechanical properties of the cups was analysed.

Formability in deep drawing and ironing process 3.1.1. OSDD and TSDD
In the OSDD and TSDD tests, the blanks with diameters of 44 mm, 46 mm and 48 mm were utilized, and the diameters of the final cups were the same.Fig. 3(a, b) and Fig. 3(c-e) show the experimental and numerical load-displacement curves under OSDD and TSDD, respectively.Fig. 3(f) demonstrates the evolution of the maximum damage value against equivalent strain in different tests.It should be noted that for the 48 mm diameter blank, fracture occurred during OSDD because the drawing ratio is out of the material's limit, while under TSDD the blank was successfully formed through redistributing the deformation.By comparing the load under OSDD and TSDD, it can be found that the maximum load of the sheet under two-stage deep-drawing forming was significantly reduced, which is conducive to reducing the tensile stress transmitted by the side wall of the cup and improving the safety margin of sheet metal forming.Meanwhile, the deformation of the cup side wall during TSDD slightly increased compared with OSDD, while the material damage was reduced.Fig. 3(g, h) present the damage and equivalent plastic strain distribution of a 44 mm diameter blank under OSDD and TSDD, respectively.The maximum damage value of the specimen in OSDD was located around the round corner of the punch, and the dangerous cross-section in TSDD was shifted from the round corner to the side wall.In TSDD, the material in the cup side wall experienced workhardening, which enhanced the loading capacity and reduced the risk of fracture.Comparing with OSDD, the deformation in TSDD was decomposed into two steps, and thereby the damage accumulation speed was alleviated.It can also be seen that as the blank diameter decreased, the maximum drawing force decreased, leading to the reduction of the damage values.

TSDDI
In TSDDI tests, the 48 mm diameter blanks were employed, and three TRRs of 13.3%, 23.3% and 33.3% were involved in the ironing stage.Fig. 4(a-c) show the load-displacement curves in the ironing stage with different TRRs.Fig. 4(d) demonstrates the maximum damage value evolution against equivalent strain under different TRRs and Fig. 4(e) presents the damage and equivalent plastic strain distributions of a 33.3% TRR blank.According to the equivalent plastic strain distribution and damage evolution of the material, it can be seen that the maximum damage value of the TSDDI cup still located at the rounded corner of the punch in the first stage deep drawing.and equivalent plastic strain distributions of blank with 33.3% TRR.

Results of damage evaluation tests
Fig. 5(a, b) respectively show the load-displacement curves of the ring specimens obtained from the cups under OSDD, TSDD, and TSDDI tests.It can be seen that the load displacement curves contain an initial slow rise stage, a rapid rise stage and a drop stage.The initial slow rise stage shows a brief nearlinear growth, corresponding to the straightened process of the deformation region on the ring specimen.
The rapid rise stage is characterized by a rapid growth of the load until reaching the maximum load point, indicating that the tensile specimen enters a stable deformation stage; the drop stage represents that the tensile specimen starts diffused necking and localized necking, and the load begins to decrease until the specimen fractures.In this study, the load Fmax and displacement x corresponding to the maximum load point of the ring tension test, as well as the displacement difference dx between the maximum load point and the fracture onset point are considered as indicators for measuring the loading capacity and deformation capacity of the plates, in which Fmax and x are considered to be tensile strength related and dx is considered to be ductility related.The average values of damage and deformation at the middle position on the cup side wall and the measures of subsequent loading capacity Fmax, x and dx of the cups corresponding to the different tests are listed in Table 2.
For OSDD and TSDD, the drawn cups had the same diameter, and the damage and deformation strain could be considered as the main influence factors for the difference in the mechanical properties of the ring tension specimens.For the same forming process, i.e., either OSDD or TSDD tests, a blank with a smaller initial diameter has a lower damage value and lower deformation, resulting in a higher Fmax, x and dx, and a better tensile strength, ductility and loading capacity.In comparing the different forming methods, it is found that before reaching the peak force, due to the comparable deformation degree of ring specimens of the OSDD and TSDD cups, the load-displacement curves have similar evolution trends.However, for blanks of the same diameter after the two kinds of deep drawing forming processes, the three measurement indicators are higher in TSDD.This result is attributed to the fact that the proper distribution of the drawing coefficients in TSDD improves the forming capacity of the material, leading to a lower damage value after deep drawing and an increase in the subsequent deformation capacity of the part.Meanwhile, for both OSDD and TSDD, it is observed that the lower the damage value, the higher the measurement index Fmax and x, i.e., the better its subsequent tensile strength.For the ring specimens cut from the cups under TSDDI tests, in combination with the data in Table 2, it can be found that with the increase of the TRR, the deformation and damage value of the cup both increased.The more significant work hardening caused the ring specimens requiring greater loading forces at the same displacement.Meanwhile, the subsequent loading capacity of the cup is weaker, leading the decrease of Fmax, x and dx.When combining the results under the OSDD, TSDD and TSDDI three different deep drawing forming methods, it can be observed that overall, the lower the damage value, the higher the Fmax, i.e., the better the subsequent tensile capacity of the part.However, the change in dx is not regular, and it may be necessary to consider the effect of factors such as the deformation degree on the subsequent ductility.

Summary and Outlook
In this paper, three types of deep drawing tests including OSDD, TSDD, and TSDDI were conducted and the damage distribution of the cups were determined based on simulations.Through comparing the performance of ring specimens cut from different drawn cups in the tension test.It is concluded that for the blank with same diameter the deformation of the cup side wall under TSDD was slightly larger than that under OSDD, while the damage value under TSDD was less.Under the same forming process, the equivalent plastic strain and damage value of the sidewall of the cup both increased with the increase in blank diameter.For TSDDI, as the TRR increased, the maximum damage value of the cup increased; the increased hydrostatic compressive stress resulted in a more homogeneous deformation of the sidewall.The ring tensile tests on deep-drawing formed parts revealed that, in general, under the same deep drawing method, the lower the damage value, the higher the subsequent tensile strength and ductile properties of the part.After comparing the result of the different drawing methods, the lower the damage value, the higher its maximum load, while the displacement difference between the maximum load point and the fracture onset point is not necessarily higher, which may be related to factors such as the degree of deformation and so on.
For the multi-stage forming process where deformation is under a nonlinear strain path, the material may need to be characterized using a more suitable constitutive model.Therefore, follow-up work could investigate the changes in the mechanical behavior of materials under complex loading paths and the effect on damage accumulation to improve the accuracy of the model in predicting the fracture behavior.

Acknowledge
This research was supported by Shanghai Outstanding Academic Leaders Plan (21XD1422000).

Figure 3 .
Figure 3. Load-displacement curves of OSDD tests: (a) blank with a diameter of 44 mm and (b) blank with a diameter of 46 mm; load-displacement curves of TSDD tests: (c) blank with a diameter of 44 mm, (d) blank with a diameter of 46 mm, (e) blank with a diameter of 48 mm; (f) damage evolution in different tests; damage and equivalent plastic strain distributions of 44mm diameter sheets: (g) after OSDD test and (h) after TSDD test.Because in the ironing forming process the die clearance is smaller than the blank thickness, the thickness direction of the blank is subjected to compressive stress.Hydrostatic compressive stress can reduce the additional tensile stress caused by the inhomogeneous deformation, thus making the deformation more homogeneous.As the TRR increased, the maximum load as well as the plastic deformation increased, leading to the increase in the damage value.The tensile stress transmitted to the cup side wall was easier to exceed the loading capacity under larger TRRs.

Figure 5 .
Figure 5. Load-displacement curves of ring-shaped specimens cut from cups in (a) OSDD and TSDD tests, and (b) TSDDI tests.

Table 2 .
Summary of damage values, deformation at the middle position on the side wall and Fmax, x and dx under ring tension test of each deep drawn cup